I am trying to improve our DNA sequencing work-flow. I choose a software called AdapterRemoval for quality trimming and merging overlapping reads. I try to benchmark AdapterRemoval against the previous software called sickle with the same parameter and I don't understand why I have so many difference.

this is the sickle command with the minimum quality of 20 and minimum read length of 30 :

It's extremely likely that these tools work somewhat differently for determining exactly where to trim things (all trimmers works slightly differently), so I'm not surprised that you get different results with the same settings. You'll need to look through the code for each if the exact reasons are really important to you.

It could be worth running post trimming process, and compare end results: length [mean, median, max, min], read/contigs, and other attributes from both tools. Just a thought. Different tools have different approach, same parameters may or may not yield same results.